Vortex-induced vibrations (VIV) in systems with more than one degree of freedom often present complex synchronization among the motion components, also hidden by the randomness that characterizes the motion itself. A phase average method has been here developed and applied to the displacements of a tethered sphere, at low mass and damping, to analyze its xy trajectories over a wide range of reduced velocities, 5 ≤ U* ≤ 25 (Reynolds numbers, 5.1 × 103 ≤ Re ≤ 2.67 × 104). This method has allowed the identification of both the periodic and chaotic contribution of each motion component, accurately reconstructing the underlying trajectory periodic pattern. The two classical vibration modes, I and II, have been also observed. The method developed...